(Received January 18, 1950)
In the first part of this paper, we treated the general property of
self-energy and self-stress of Fermion and Boson in usual perturbation
formalism, and found the general relation
<\overset°Tµµ>= m (∂/(∂ m))<\overset°T44>+ µ(∂/(∂µ)9<\overset°T44>
between them, which holds for Fermion with mass m interacting with Boson with mass µ, and vice versa. The fact that the self-stress can be expressed as surface-integral in k4-space was shown in the last paragraph. We now want to show that they can be reduced to the two dimensional surface in k(3)-space, and that the numerical value of them depends on the shape of surface taken. The same results as in I can be obtained by chosing the surface spherically. And it was also shown that the self-stress only contains as diverging quantity the multiple of the surface area of k(3)-space, no logarithmic divergences. In §3, a physical interpretation of expectation value of stress-tensor, which has analogous meaning as classical Poincare tensor, is given. And, finally, we want to seek for the relation between convergence condition of self-energy and stability condition of particle from the three different standpoints, founding that the formalistic regularization is to be modified to be effective for stabilization problem.
URL : http://ptp.ipap.jp/link?PTP/5/236/
DOI : 10.1143/PTP.5.236